A233265 Prime(k), where k is such that (1 + Sum_{j=1..k} prime(j)^12) / k is an integer.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 37, 41, 43, 47, 53, 61, 71, 73, 89, 101, 103, 107, 113, 149, 151, 167, 173, 181, 197, 199, 223, 239, 251, 263, 281, 307, 313, 317, 349, 359, 397, 409, 433, 449, 463, 467, 541, 569, 571, 613, 643, 659, 701, 733, 787, 809

Offset: 1

Author

Robert Price, Dec 06 2013

Keywords

• nonn

Comments

a(1171) > 661876608760109. - Bruce Garner, Jun 06 2021

Examples

			a(4) = 7, because 7 is the 4th prime and (1 + Sum_{i=1..4} prime(i)^12) / 4 = 14085963364/4 = 3521490841 which is an integer.
		

Links

• Bruce Garner, Table of n, a(n) for n = 1..1170 (terms 1..907 from Robert Price, terms 908..967 from Karl-Heinz Hofmann)
• OEIS Wiki, Sums of powers of primes divisibility sequences

Crossrefs

Cf. A085450 (smallest m > 1 such that m divides Sum_{k=1..m} prime(k)^n).

Cf. A007504, A045345, A171399, A128165, A233523, A050247, A050248.

Cf. A024450, A111441, A217599, A128166, A233862, A217600, A217601.

Programs

Maple

A233265:=n->if type((1+add(ithprime(i)^12, i=1..n))/n, integer) then ithprime(n); fi; seq(A233265(k),k=1..200); # Wesley Ivan Hurt, Dec 06 2013

Mathematica

t = {}; sm = 1; Do[sm = sm + Prime[n]^12; If[Mod[sm, n] == 0, AppendTo[t, Prime[n]]], {n, 100000}]; t (* Derived from A217599 *)
Prime[#]&/@(Flatten[Position[#[[1]]/#[[2]]&/@With[{nn=200},Thread[ {(Rest[ FoldList[ Plus,0,Prime[Range[nn]]^12]])+1,Range[nn]}]],?IntegerQ]]) (* _Harvey P. Dale, Nov 19 2018 *)

PARI

is(n)=if(!isprime(n),return(0)); my(t=primepi(n),s); forprime(p=2,n,s+=Mod(p,t)^12); s==0 \\ Charles R Greathouse IV, Nov 30 2013